A. We begin by studying the surface area of an ellipsoid in E as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over Sn−1, use this formula to derive convexity properties of the surface area, to give sharp estimates for the surface area of a large-dimensional ellipsoid, to produce asymptotic formulas for the surface area and the isoperimetr...

Define a cubical complex to be a collection of integer-aligned unit cubes in d dimensions. Lebowitz and Mazel (1998) proved that there are between (C1d) and (C2d) complexes containing a fixed cube with connected boundary of (d − 1)volume n. In this paper we narrow these bounds to between (C3d) and (C4d). We also show that there are nn/(2d(d−1))+o(1) connected complexes containing a fixed cube w...

27. Holt Geometry. All rights reserved. Name. Date. Class. LESSON. 10-4. Practice A. Surface Area of 3. surface area of a right prism with lateral area L and base area B. S. L. 2B. 4. surface . Give your answers in terms of . 9. 2 in. 2 in. 10. a . understanding thermal relations between swine and their SA=970 W "633, where SA=swine body sur. Hence, part of the difference between Brody's. find ...

Measures of erythrocytes volume and surface are helpful in several physiological studies, both for zoologists and veterinarians. Whilst diameter and volume are assessed with ease from observations of blood smears and complete blood count, respectively, thickness and surface area, instead, are much more difficult to be obtained. The accurate description of the erythrocyte geometry is given by th...

Electron microscopy was used to measure microvillous surface area in seven small intestinal biopsies showing secondary disaccharidase deficiency and in five biopsies having normal disaccharidase levels. There were significant reductions in microvillous surface area in the enzyme deficient group, although the microvilli were not severely damaged. Histological abnormality was not always present w...

Surface area of discrete objects is an important feature for model-based image analysis. In this article, we present a theoretical framework in order to prove multigrid convergence of surface area estimators based on discrete normal vector field integration. The paper details an algorithm which is optimal in time and multigrid convergent to estimate the surface area and a very efficient algorit...

Biochemists often wish to compute surface areas of proteins. A variety of algorithms have been developed for this task, but they are designed for traditional single-processor architectures. The current trend in computer hardware is towards increasingly parallel architectures for which these algorithms are not well suited. We describe a parallel, stochastic algorithm for molecular surface area c...

A dual capacitary Brunn-Minkowski inequality is established for the (n − 1)capacity of radial sums of star bodies in R. This inequality is a counterpart to the capacitary Brunn-Minkowski inequality for the p-capacity of Minkowski sums of convex bodies in R, 1 ≤ p < n, proved by Borell, Colesanti, and Salani. When n ≥ 3, the dual capacitary BrunnMinkowski inequality follows from an inequality of...

The specific surface area of a powder is determined by physical adsorption of a gas on the surface of the solid and by calculating the amount of adsorbate gas corresponding to a monomolecular layer on the surface. Physical adsorption results from relatively weak forces (van der Waals forces) between the adsorbate gas molecules and the adsorbent surface of the test powder. The determination is u...